Character animation has become increasingly sophisticated. For example, besides just animating the movements of characters, character bodies animate within themselves, e.g., deforming in response to character movements and collisions. For example, deformation parameters may provide for bulging of skin surfaces when a character flexes a joint.
More sophisticated techniques for skin deformation include the simulation of muscles. The muscles may be defined by a geometry with control points, and collision detection may be employed to move or to deform the muscle geometry as muscles interact with bones or other muscles.
However, such techniques have not to date resulted in satisfactory visual effects in all circumstances. For example, complicated dynamic simulations, e.g., those employing continuum mechanics, where elements in a subsequent frame are calculated by consideration of forces on objects in a prior frame, are computationally intensive and highly inconvenient.